Решите уравнения: a) 5 1/3 x - 1 = 1 2/9;

### Левый столбец 1. $5\frac{1}{3}x - 1 = 1\frac{2}{9}$ $5\frac{1}{3}x = 2\frac{2}{9}$ $\frac{16}{3}x = \frac{20}{9}$ $x = \frac{20}{9} : \frac{16}{3} = \frac{20}{9} \cdot \frac{3}{16} = \frac{5}{12}$ **Ответ: $\frac{5}{12}$** 2. $\frac{18}{49} : x = \frac{6}{35}$ $x = \frac{18}{49} : \frac{6}{35} = \frac{18}{49} \cdot \frac{35}{6} = \frac{15}{7} = 2\frac{1}{7}$ **Ответ: $2\frac{1}{7}$** 3. $4\frac{1}{12} - 1\frac{5}{6}x = 2\frac{17}{24}$ $1\frac{5}{6}x = 4\frac{1}{12} - 2\frac{17}{24} = 4\frac{2}{24} - 2\frac{17}{24} = 3\frac{26}{24} - 2\frac{17}{24} = 1\frac{9}{24} = 1\frac{3}{8}$ $x = \frac{11}{8} : \frac{11}{6} = \frac{11}{8} \cdot \frac{6}{11} = \frac{3}{4}$ **Ответ: $\frac{3}{4}$** 4. $3\frac{1}{3} : (\frac{3}{7}x - \frac{13}{15}) = 1\frac{9}{16}$ $\frac{3}{7}x - \frac{13}{15} = \frac{10}{3} : \frac{25}{16} = \frac{10}{3} \cdot \frac{16}{25} = \frac{32}{15} = 2\frac{2}{15}$ $\frac{3}{7}x = 2\frac{2}{15} + \frac{13}{15} = 2\frac{15}{15} = 3$ $x = 3 : \frac{3}{7} = 7$ **Ответ: $7$** 5. $(1\frac{7}{8}x - 2\frac{1}{3}) \cdot 24 = 4$ $1\frac{7}{8}x - 2\frac{1}{3} = 4 : 24 = \frac{1}{6}$ $1\frac{7}{8}x = \frac{1}{6} + 2\frac{1}{3} = \frac{1}{6} + 2\frac{2}{6} = 2\frac{3}{6} = 2\frac{1}{2}$ $x = \frac{5}{2} : \frac{15}{8} = \frac{5}{2} \cdot \frac{8}{15} = \frac{4}{3} = 1\frac{1}{3}$ **Ответ: $1\frac{1}{3}$** ### Правый столбец 1. $4\frac{4}{9}x + 1 = 2\frac{17}{18}$ $4\frac{4}{9}x = 1\frac{17}{18}$ $\frac{40}{9}x = \frac{35}{18}$ $x = \frac{35}{18} : \frac{40}{9} = \frac{35}{18} \cdot \frac{9}{40} = \frac{7}{16}$ **Ответ: $\frac{7}{16}$** 2. $\frac{27}{56} : x = \frac{9}{32}$ $x = \frac{27}{56} : \frac{9}{32} = \frac{27}{56} \cdot \frac{32}{9} = \frac{3 \cdot 4}{7} = \frac{12}{7} = 1\frac{5}{7}$ **Ответ: $1\frac{5}{7}$** 3. $4\frac{1}{15} - 1\frac{14}{15}x = 1\frac{1}{6}$ $1\frac{14}{15}x = 4\frac{1}{15} - 1\frac{1}{6} = 4\frac{2}{30} - 1\frac{5}{30} = 3\frac{32}{30} - 1\frac{5}{30} = 2\frac{27}{30} = 2\frac{9}{10}$ $\frac{29}{15}x = \frac{29}{10}$ $x = \frac{29}{10} : \frac{29}{15} = \frac{15}{10} = 1\frac{1}{2}$ **Ответ: $1\frac{1}{2}$** 4. $4\frac{4}{9} : (\frac{2}{3}x + 14) = \frac{5}{27}$ $\frac{2}{3}x + 14 = \frac{40}{9} : \frac{5}{27} = \frac{40}{9} \cdot \frac{27}{5} = 8 \cdot 3 = 24$ $\frac{2}{3}x = 24 - 14 = 10$ $x = 10 : \frac{2}{3} = 15$ **Ответ: $15$** 5. $30 \cdot (1\frac{5}{6}x + 3\frac{1}{5}) = 231$ $1\frac{5}{6}x + 3\frac{1}{5} = 231 : 30 = 7,7$ $1\frac{5}{6}x = 7,7 - 3,2 = 4,5$ $\frac{11}{6}x = \frac{9}{2}$ $x = \frac{9}{2} : \frac{11}{6} = \frac{9}{2} \cdot \frac{6}{11} = \frac{27}{11} = 2\frac{5}{11}$ **Ответ: $2\frac{5}{11}$**